MIAMI BEACH, Florida (Reuters) - Six same-sex couples sued the state of Florida on Tuesday to overturn its ban on gay marriage, joining dozens of lawsuits in other states that argue such prohibitions violate the U.S. Constitution.

The lawsuit, filed in Miami-Dade County Circuit Court, contends that Florida's ban denies same-sex couples the legal protections and "equal dignity" that come with marriage. The ban was added to the state's constitution in 2008 after approval by voters.

"These laws are out of step and outdated," said Shannon Minter, legal director of the National Center for Lesbian Rights, which is representing the couples. Minter added that similar suits have been filed in North Carolina, Tennessee and Michigan.

Since the Supreme Court's 2013 decision overturning the Defense of Marriage Act forced the federal government to recognize same-sex marriages in states where they are legal, same-sex couples and advocacy groups have brought more than 40 lawsuits, Minter said.

Gay marriage in Florida could become major issue in elections in November. Florida Governor Rick Scott, a Republican, has said he believes in "traditional marriage."

His likely challenger, former governor Charlie Crist, a one-time Republican now running for the office again as a Democrat, said Tuesday he supports the lawsuit.

As governor, Crist backed the constitutional ban, but he recently came out in support of gay marriage and apologized for his previous position. "I'm proud to support the lawsuit challenging Florida's ban on marriage equality, it's an issue of fairness," he Tweeted.

Utah's state tax commission last week said the 1,400 same-sex couples who married after a federal judge there struck down the state's ban on gay marriage as unconstitutional could jointly file their state income taxes. Utah is appealing the decision striking down the ban and the Supreme Court issued a stay on gay marriages while the appeal is under way.

Advocates for same-sex marriage in Florida argue support has grown significantly since 2008, when 62 percent of the state's voters approved the constitutional amendment banning same-sex marriage. A 2013 poll by the Public Religion Research Institute showed a majority of Floridians, 54 percent, supported same-sex marriage.

The poll also showed a slightly smaller majority of Americans, 52 percent, approved of gay marriage.

FIGHT PROMISED

"We wanted our son to be born into a family that felt like every other family," Todd Delmay, a plaintiff along with his partner, Jeff, told a Tuesday morning press conference on Miami Beach announcing the lawsuit.

"The time is right, the time is now, and we look forward to having the right and the freedom to marry."

Supports of the ban, on the other hand, vowed to fight any attempt to reverse it.

After losing the 2008 vote "gay activists ... have resorted to trying to find renegade courts who have little respect for the rule of law to create social change that would never happen through the people or their elected representatives," said John Stemberger, an Orlando attorney who is president of the Florida Family Policy Council and led the 2008 campaign to ban gay marriage.

"We will not sit idly by and watch leftist groups try to undermine this," he added.

(Reporting by Bill Cotterell in Tallahassee; Editing by David Adams, Cynthia Osterman and Steve Orlofsky)